The curve represented by the equation r = a, where a is a constant, is called the spiral of Archimedes. (a) Use a graphing utility

The curve represented by the equation r = aθ, where a is a constant, is called the spiral of Archimedes.

(a) Use a graphing utility to graph r = θ, where θ ≥ 0. What happens to the graph of r = aθ as a increases? What happens if θ ≤ 0? 

(b) Determine the points on the spiral r = aθ (a > 0, θ ≥ 0), where the curve crosses the polar axis. 

(c) Find the length of r = θ over the interval 0 ≤ θ ≤ 2π. 

(d) Find the area under the curve r = θ for 0 ≤ θ ≤ 2π.